The crucial quantity behind the s XY criticality is the exponent is of microscopic nature in the sense that it does not involve the Kane–Fisher renormalization of the links/scratches, nor the system size.
(In the 2D classical case, the analog of the Kane–Fisher renormalization is the renormalization due to the thermal fluctuations of the phase field across the scratch.) The most spectacular manifestation of the special role played by Since the size of the link gets progressively larger for weaker links (if the barrier height is limited, its length has to increase), the RG flow is formulated in the space of system sizes rather than distances. In the present work, we focus on solving two outstanding problems of the s XY criticality: (i) a qualitative and quantitative understanding of the interplay between the s XY and GS scenarios in the vicinity of corresponding tri-critical point on the SF–BG phase boundary and (ii) applying the theory to the disordered Bose–Hubbard model with no spatial correlation.
Without loss of generality, the hopping amplitude is set equal to unity. Given the exponential divergence of the correlation length on approach to the quantum critical point, brute-force numerical and experimental approaches to reveal the thermodynamic limit properties are out of the question.
An integral part of the numeric analysis is extracting the exponent from statistically rare disorder realizations in samples of moderate sizes.
The new weak-link universality class is termed 'scratched-XY criticality (s XY)' because, under the standard 1D-quantum-to-2D-classical mapping, it corresponds to the SF-normal phase transition in the 2D classical XY model with correlated disorder in the form of parallel 'scratches' (Josephson barriers).
At high enough disorder strength, the s XY criticality preempts the BKT transition.
A 'strong-disorder' alternative therefore seems unlikely. Nevertheless, Altman , inspired by the 1D-specific classical-field mechanism of destroying global SF stiffness by anomalously rare but anomalously weak links, speculated that an alternative strong-disorder scenario does exist .
To corroborate their idea, the authors employed a real-space RG treatment.The difference is in the classical-field mechanism of suppressing the SF stiffness by weak links (for a discussion, see [9, 11]): in a single weak link cannot destroy superfluidity, the combined effect of all anomalously weak links in suppressing Λ may be strong enough at large system sizes to drive the system into an insulating state at , when the generic instanton–anti-instanton pair dissociation mechanism remains irrelevant.